# Problems from Computation of images and inverse images

Consider the function $$f$$ defined by three plus the root of a given real number. Find its analytical expression as well as $$f (1), f (4)$$ and $$f^{-1}(7)$$.

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### Development:

We write the algebraic expression of the function:

$$f(x)=\sqrt{x}+3$$$We can calculate now: $$f(1)=\sqrt{1}+3=1+3=4$$$ $$f(4)=\sqrt{4}+3=2+3=5$$$$$f^{-1}(7):$$$ $$7=\sqrt{x}+3$$$$$4=\sqrt{x}$$$ $$x=16$$\$

### Solution:

$$f(x)=\sqrt{x}+3$$

$$f(1)=4$$

$$f(4)=5$$

$$f^{-1}(7)=16$$

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